Journal article 1512 views
Line bundles and the Thom construction in noncommutative geometry
,
Tomasz Brzeziński,
Tomasz Brzezinski
Journal of Noncommutative Geometry, Volume: 8, Issue: 1, Pages: 61 - 105
Swansea University Authors:
Edwin Beggs , Tomasz Brzezinski
Full text not available from this repository: check for access using links below.
DOI (Published version): 10.4171/JNCG/149
Abstract
The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we c...
| Published in: | Journal of Noncommutative Geometry |
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| ISSN: | 1661-6952 1661-6960 |
| Published: |
2014
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa13888 |
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| Abstract: |
The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we construct a positive integer graded module. This corresponds to the topological Thom construction and associated circle bundle for a line bundle. In the case that the original algebra is a C* algebra, with some positivity assumptions, the Thom construction gives another C* algebra.The paper ends by a study of the de Rham characteristic classes of a NC line module using the methods of Kobayashi and Nomizu. |
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| Item Description: |
Accepted for publication May 2012. |
| Keywords: |
Noncommutative geometry, line bundle, Chern class, Thom construction |
| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
61 |
| End Page: |
105 |